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On Central Cantor Sets with Self‐Arithmetic Difference of Positive Lebesgue Measure
Author(s) -
Bamón Rodrigo,
Plaza Sergio,
Vera Jaime
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/52.1.137
Subject(s) - mathematics , measure (data warehouse) , lebesgue measure , cantor function , arithmetic , lebesgue integration , lebesgue–stieltjes integration , pure mathematics , discrete mathematics , cantor set , riemann integral , computer science , data mining , operator theory , fourier integral operator
We prove the existence of C r ‐ (but not C r +1 ‐) regular central Cantor sets with zero Lebesgue measure such that their self arithmetic difference is a Cantor set with positive Lebesgue measure. This is motivated by a conjecture in the field of bifurcations of dynamical systems posed by Jacob Palis.